Preferential duplication graphs

We consider a preferential duplication model for growing random graphs, extending previous models of duplication graphs by selecting the vertex to be duplicated with probability proportional to its degree. We show that a special case of this model can be analysed using the same stochastic approximation as for vertex-reinforced random walks, and show that 'trapping' behaviour can occur, such that the descendants of a particular group of initial vertices come to dominate the graph

Democratizing the FLSA Injunction: Toward a Systemic Remedy for Wage Theft

The Fair Labor Standards Act (FLSA) and its state equivalents have proven a regulatory failure, as their minimum wage and overtime protections are widely violated with impunity. This Note attributes that failure partly to the overlooked issue of private injunctive relief. FLSA and most state laws reserve injunctive relief for agency actions - a remedial limitation that reflects New Deal regulatory attitudes presuming agency-centered enforcement, from which Title VII and other statutes have since diverged. Public enforcement is clearly insufficient to address the epidemic in wage and hour violations, and FLSA\u27s private enforcement regime of retrospective damages actions effectively treats wage theft as a matter of individualized malice

Simplicity and maximal commutative subalgebras of twisted generalized Weyl algebras

In this paper we show that each non-zero ideal of a twisted generalized Weyl algebra (TGWA) $A$ intersects the centralizer of the distinguished subalgebra $R$ in $A$ non-trivially. We also provide a necessary and sufficient condition for the centralizer of $R$ in $A$ to be commutative, and give examples of TGWAs associated to symmetric Cartan matrices satisfying this condition. By imposing a certain finiteness condition on $R$ (weaker than Noetherianity) we are able to make an Ore localization which turns out to be useful when investigating simplicity of the TGWA. Under this mild assumption we obtain necessary and sufficient conditions for the simplicity of TGWAs. We describe how this is related to maximal commutativity of $R$ in $A$ and the (non-) existence of non-trivial $\Z^n$-invariant ideals of $R$. Our result is a generalization of the rank one case, obtained by D. A. Jordan in 1993. We illustrate our theorems by considering some special classes of TGWAs and providing concrete examples.Comment: 32 pages, no figures, minor improvements of the presentation of the materia

The emission line near 1319 A in solar and stellar spectra

An emission line near 1319 A is one of the strongest unidentified lines in the ultraviolet spectra of cool dwarf stars. In most line lists it is identified as a transition in N I, although its intensity would then be anomalous and the observed wavelength does not fit precisely that expected for N I. The line is also observed in cool giant stars. The measured wavelength of the line in stellar spectra is 1318.94 (+,- 0.01) A. Observations of giant stars provide further evidence that this line is not due to N I. It is proposed that this line is a decay from a previously unknown level in S I, which lies above the first ionization limit. This is identified with the 3d singlet D (odd parity) term. The previous tentative assignment of this term to the S I line at 1309.3 A then needs to be revised. The 1309.3 A line has been identified here for the first time in an astrophysical source. The singlet D (odd parity) level could, in principle, be populated by collisions from nearby autoionizing levels that have large number-densities, through population by di-electronic capture. Spin-orbit interaction with the autoionizing triplet D (odd parity) term might also lead to di-electronic capture into the singlet D (odd parity) level. A line at 1309.87 A observed in cool giant stars is identified as a transition in P II, pumped by the O I resonance lines.Comment: 9 pages, 3 figures, to be published in Monthly Notices of the Royal Astronomical Societ

Gait Modulation in C. elegans: An Integrated Neuromechanical Model

Equipped with its 302-cell nervous system, the nematode Caenorhabditis elegans adapts its locomotion in different environments, exhibiting so-called swimming in liquids and crawling on dense gels. Recent experiments have demonstrated that the worm displays the full range of intermediate behaviors when placed in intermediate environments. The continuous nature of this transition strongly suggests that these behaviors all stem from modulation of a single underlying mechanism. We present a model of C. elegans forward locomotion that includes a neuromuscular control system that relies on a sensory feedback mechanism to generate undulations and is integrated with a physical model of the body and environment. We find that the model reproduces the entire swim-crawl transition, as well as locomotion in complex and heterogeneous environments. This is achieved with no modulatory mechanism, except via the proprioceptive response to the physical environment. Manipulations of the model are used to dissect the proposed pattern generation mechanism and its modulation. The model suggests a possible role for GABAergic D-class neurons in forward locomotion and makes a number of experimental predictions, in particular with respect to non-linearities in the model and to symmetry breaking between the neuromuscular systems on the ventral and dorsal sides of the body